Solving singular boundary value problems using higher-order compact finite difference schemes with a novel higher-order implementation of Robin boundary conditions

Abstract

This study introduces a novel and very accurate method for implementing Robin boundary conditions while solving boundary value problems with compact finite difference schemes. Most studies numerically approximate Neumann and Robin boundary conditions with a first-order approximation, however, this reduces the accuracy in general. Our implementation produces highly accurate results in solving nonlinear singular boundary value problems. Other reported results achieved utilizing various techniques are used for comparison. Tables and graphs showing the results are given.